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Surprisingly it's quite easy to answer this because we can use the cosmic microwave background as a reference. The CMB gives us an average inertial frame for the universe so our motion relative to it is the closest we can come to defining the Solar System's motion through space. The CMB is isotropic, but because we are moving relative to it the radiation is ...


$ L = \int \int {\bf F} \cdot d{\bf s}$ is where you should start, where $F$ is the flux in units of Watts/m$^2$. Blackbody flux is given by $\sigma T^4$ and hence an isotropic flux integrated over a sphere $$ L \int^{2\pi}_{0} \int^{\pi}_{0} \sigma T^4 r^2 \sin \theta\, d\theta\,d\phi = 4\pi r^2 \sigma T^4$$

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